Stat 328 Lab #4 Summer 2000
On the Stat 328 Web Page you will find a fairly large data set titled "Wisconsin Restaurant
Data." There are 181 cases of responses made on the 1980 Wisconsin Restaurant Survey
conducted by the University of Wisconsin Small Business Development Center. Recorded are
values for:
"outlook"
"sales"
"newcap"
"value"
"costgood"
"wages"
"ads"
"typefood"
"seats"
"owner"
"FTemploy"
"PTemploy"
"size"
a business outlook rating (" œ very unfavorable to ( œ very favorable)
gross 1979 sales ($"!!!)
new capital invested in 1979 ($"!!!)
estimated market value of the business ($"!!!)
cost of goods sold as a percentage of the sales
wages as a percentage of sales
advertising as a percentage of sales
a code for type of food sold (" œ fast food, # œ supper club, $ œ other)
number of seats in the dining area
a code for type of ownership (" œ sole proprietorship, # œ partnership,
$ œ corporation)
number of full time employees
number of part time employees
a code summarizing the number of employees (" œ " to *Þ& employees, # œ "! to
#! employees, $ œ over #! employees, where a part time employee counts as Þ&)
Download the data set and read it into JMP.
Your fundamental task is to build an effective model for "sales" in terms of the other variables.
You have at your disposal JMP, all you've learned about MLR, and your good business sense.
You may:
• transform any variable(s)
• make up new predictors from the ones above (for example, allowing for interactions that
you expect on the basis of what you know about business, or combining variables into a
single one ... for example replacing all of the last $ predictors with
FTemploy € Þ&ÐPTemployÑ looks to me like it might be sensible)
Your search should consider issues such as parsimony/simplicity of the final model you settle on,
the possibility that a few unusual cases dominate the fitting of the model and should really be
eliminated from the fitting, goodness of fit criteria like V # ß T VIWWß Q WI and G: , sensiblelooking residuals, etc. Be sure that if you use the qualitative variables above in your analysis,
you handle them in a sensible manner (for example, you surely don't want to treat the codes for
"typefood" as if they were values of a measured variable).
When you have settled on a model you'd be willing to use in a report to the Governor of
Wisconsin (about variables related to revenue for restaurants in the state) compute and plot
residuals against all of the predictors and against sC, and normal plot them as means of model
checking. Then make 95% prediction limits for all the different sets of predictors you retain in
your data set. (If you end up modeling a transform of C, compute the limits on the transformed
scale and then "untransform" them to get limits on the original scale.) How do your predictions
agree with the original C's? Write a paragraph or two interpreting your model (to the extent that
is possible) to the proverbial "layman." (What variables are the best predictors of revenue, etc.)
There is (obviously) no "right" answer here. Do something sensible and document and defend it.